G. PLARR ON THE SOLUTION OF THE EQUATION Vpgp=0 : 65 
will give three real positive values for ¢’ for those values of E comprised 
between the above limits of E, namely 
between h, and he =e, 
which both are comprised between the general limits of E, namely, between 
h, and h,. 
§ 9. When we consider E as a parameter on which the values of ¢’ depend 
by the equation F(e’)=0, then the directions «’ = Ue, corresponding to a given 
value of E, will represent the generating lines of a cone of the 2d order, 
according to the formula (51 bis), in which E is supposed constant and ¢’ vari- 
able in direction. 
For the extreme limits E=h, and E=h/, the cone reduces itself to the 
straight lines ) and v respectively. 
For E=h,, the cone reduces itself to two planes passing through p, the 
angles n, of the normal to these planes with the axis v, as for example, being 
tg Ny = oe =) y= 

Let us designate these planes by R, R’. 
When A, is positive, then the cone corresponding to E = E, will be 
comprised in the angles of R and R’ which contain the axes v, and —», 
because then we have 
Meeps 
and E beginning to grow from /; (which is negative) by degrees up to hf, , will 
reach E, before it reaches h, . 
When h, is negative, then the cone corresponding to E=E, will be com- 
prised in the angles of the above planes in which the axis \ and —) are situated, 
because then A,< E,;< 0. 
For E=E, the equation of the corresponding cone takes the more simple 
form : . 
(51 ter) O= TS, namely Sea’ = 0, 
because we have 
Eh (1 = iP) = La(P’—2h). 
and P’—Ayhs=hy(hy + hs) = je, a ee —hi: P’ ) &e. 
VOL. XXVIII. PART I. R 


